Eur. Phys. J. B (2012) 85: 353
https://doi.org/10.1140/epjb/e2012-30388-3

Regular Article

Hydrogenic impurity states in a spherical quantum antidot: Spin-orbit interaction, relativistic correction, and diamagnetic susceptibility

¹ Department of Physics, College of Sciences, Yasouj University, 75914-353 Yasouj, Iran
² Department of Physics, College of Sciences, Shiraz University, 71454 Shiraz, Iran

^a e-mail: khordad@mail.yu.ac.ir

Received: 16 May 2012
Received in final form: 10 July 2012
Published online: 22 October 2012

Abstract

In the present work, we study three characteristics of a hydrogenic impurity located at the center of a GaAs/Ga_1−xAl_xAs spherical quantum antidot within the effective mass approximation. These characteristics are the diamagnetic susceptibility, the spin-orbit interaction (SOI), and the relativistic correction (RC). First we outline the analytic solution of the corresponding Shrödinger equation with a hydrogenic impurity at the center and obtain the energy levels and wave functions. The results obtained from the present work reveal that the diamagnetic susceptibility increases with increasing the antidot size for finite barrier. The mean value of r² increases when the antidot size increases. The SOI and RC increase by increasing the concentration. The RC and SOI approach to zero when the antidot size increases. The splitting between j = 1/2 and 3/2 due to the SOI decreases by increasing antidot size.